The German state of Bavaria has struck a sour note with the family of celebrated classical composer Felix Mendelssohn by refusing to return a precious Picasso painting lost during the Nazis’ pre-Holocaust persecution of German Jews.

Three of Mendelssohn’s relatives are suing Bavaria over “Madame Soler,” a 1903 portrait from the artist’s popular “Blue Period” that’s worth an estimated $100 million.

The plaintiffs include Britt-Marie Enhoerning, who holds both American and Swedish citizenship and has a home in Queens. Their Manhattan federal-court suit says “Madame Soler” was formerly owned by Paul von Mendelssohn-Bartholdy, a Berlin banker of Jewish descent and a relative of the 19th-century composer famed for his overture for “A Midsummer Night’s Dream.”

Beginning in the early 1900s, Mendelssohn-Bartholdy amassed a “singular private modern art collection” of about 60 works by pre-eminent painters including Picasso, van Gogh, Monet and Renoir, court papers say.

But after the Nazis took over Germany and began to eradicate Jewish-owned banks, — decimating his cash flow — Mendelssohn-Bartholdy began liquidating his collection before dying of a heart attack in 1935.

“Madame Soler” was consigned to Berlin art dealer Justin Thannhauser, who fled Germany in 1937 and sold it out of his Manhattan apartment in 1964 to the Bavarian State Paintings Collection “through its agent and incoming director,” who’s identified in the suit as “former Nazi party member Halldor Soehner.”

“When it acquired ‘Madame Soler’ in 1964, Bavaria was planning to sell secretly some 113 paintings that leading former Nazi officials like Herman Göring and Martin Bormann had owned, and to auction these works to unsuspecting buyers to raise money to acquire modern artworks like ‘Madame Soler,’” court papers charge.

“With ex-Nazi Halldor Soehner directing operations, Bavaria auctioned 106 of these works in 1966-67 by concealing the ownership history of these paintings so that prospective buyers remained unaware that notorious Nazi leaders once had owned them — and that the Nazis in turn may have acquired these works from persecuted Jews.”

Although Mendelssohn-Bartholdy’s heirs previously won a $5 million settlement after suing the Museum of Modern Art and the Guggenheim over two other Picassos from his collection, The suit says Bavaria has refused to return “Madame Soler” or submit the dispute to Germany’s Limbach Commission, which hears claims over Nazi-looted art.

“This is a case of great historical importance involving Germany’s most famous Jewish family,” plaintiffs’ lawyer John Byrne Jr. said.

“We are perplexed and disappointed by Bavaria’s failure to properly address the important issues involved in this matter,” plaintiffs lawyer John Byrne Jr. said.